Single-grain age measurements have become a popular way to investigate detrital sedimentary provenance. Such studies must fulfill an important condition that the measured sample is representative of the total detrital population. Dodson et al. [1] argue that at least k=60 grains must be measured to reduce the chance to less than p=5% that one particular fraction (in their case, the oldest) of the population is missed if this fraction is greater than f=0.05, according to:
This equation has been used incorrectly (e.g.
[2,3]) to imply that 60 grains would be enough
to have 95% confidence that any fraction f
0.05 of the
population was not missed. It will be shown why this is not true (a
proof is given in Appendix A), and an alternative will be developed
for studies that are interested in all age components, rather
than just one. While some studies use 60 grains for the wrong reason,
other authors have used even fewer grains, thereby increasing the
likelihood of missing significant fractions of the detrital age
spectrum (e.g. [4,5]). However, it is not my
intention to suggest that these are necessarily bad studies. In
addition to making recommendations for the number of sediment grains
that should be dated in a statistically adequate provenance study,
this paper also suggests how to report data sets with fewer
measurements.
